A338882 Product of the nonzero digits of (n written in base 9).

1, 1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 2, 3, 4, 5, 6, 7, 8, 2, 2, 4, 6, 8, 10, 12, 14, 16, 3, 3, 6, 9, 12, 15, 18, 21, 24, 4, 4, 8, 12, 16, 20, 24, 28, 32, 5, 5, 10, 15, 20, 25, 30, 35, 40, 6, 6, 12, 18, 24, 30, 36, 42, 48, 7, 7, 14, 21, 28, 35, 42, 49, 56, 8, 8, 16, 24, 32, 40, 48, 56, 64

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8) * A(x^9).

Mathematica

Table[Times @@ DeleteCases[IntegerDigits[n, 9], 0], {n, 0, 80}]
nmax = 80; A[_] = 1; Do[A[x_] = (1 + x + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6 + 7 x^7 + 8 x^8) A[x^9] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Times@@(IntegerDigits[n, 9]/.(0->1)), {n, 0, 80}] (* Harvey P. Dale, Oct 08 2021 *)

Prog

(PARI) a(n) = vecprod(select(x->x, digits(n, 9))); \\ Michel Marcus, Nov 14 2020

Crossrefs

Product of the nonzero digits of (n written in base k): A000012 (k = 2), A117592 (k = 3), A338854 (k = 4), A338803 (k = 5), A338863 (k = 6), A338880 (k = 7), A338881 (k = 8), this sequence (k = 9), A051801 (k = 10).

Cf. A007095, A309788.

Sequence in context: A255829 A277547 A190598 * A053844 A010887 A101412

Adjacent sequences: A338879 A338880 A338881 * A338883 A338884 A338885

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 13 2020

Status

approved